Update: On Tuesday, Pew updated its estimate of the number of unauthorized immigrants in the U.S., estimating that the overall total remained slightly above 11 million through 2014. (The chart below has been updated.) That makes up about a quarter of all immigrants in the United States. How can they be certain of those numbers? Read on.

At the core of Donald Trump's proposals on immigration is that he hopes to crack down on immigrants here illegally. But Trump repeatedly claims not to know how many people that is.

"The central issue is not the needs of the 11 million illegal immigrants or however many there may be -- and honestly we've been hearing that number for years," he said during his speech on Wednesday. "It's always 11 million. Our government has no idea. It could be 3 million. It could be 30 million. They have no idea what the number is."

It's an important figure in part because Trump's ideas for dealing with those immigrants could balloon in cost if the number is three times the 11 million "we've been hearing for years." But Trump misunderstands the figure in a number of key ways. It's not produced by the government, it's not static at 11 million -- and there's basically no way it could be off by 300 percent.

The most common source for the 11 million figure is number-crunching from Pew Research Center. Year-by-year, Pew crafts an estimate of the country's undocumented immigrant population, using a variety of statistical tools to ensure that the figure is as accurate as possible. The detailed methodology is available online, but we spoke with Pew senior demographer Jeffrey Passel to walk us through the calculation in simpler terms.

We spoke by phone. A transcript of that discussion (lightly edited, as they say) follows.

THE FIX: How, broadly speaking, does Pew figure out how many people have immigrated here illegally?

PASSEL: We start with a fairly simple equation. We start with an estimate of the foreign-born population, and we subtract from the total foreign-born population an estimate of the immigrants who are here legally. That difference is our estimate of the unauthorized immigrant population.

The formula.

THE FIX: So the estimate for the foreign-born population comes from Census data?

PASSEL: The estimate of the total foreign-born comes from surveys that the Census Bureau does. The main one we use is the American Community Survey. We make adjustments to that survey for people who are missed in the survey.

THE FIX: How does that adjustment work?

PASSEL: There are a couple of different sources that we use. The Census Bureau itself does evaluations of how complete the census and their surveys are. So we base our estimates in part on the figures that they have for what they call the "undercount."

We also use some information from a couple of other studies that are done that look specifically at Mexican immigrants and whether or not they participated in the census. What these studies have found is that U.S.-born Mexicans are much more likely to participate than legal immigrants, who are much more likely to participate than unauthorized immigrants. So we use the Census Bureau's data as a base for our corrections, but we make adjustments for what we know to be higher undercounts of legal immigrants and then yet higher undercounts of unauthorized immigrants.

As a check on all of this, we also are able to look at data mainly from Mexico on the number of Mexicans in Mexico. Basically all of the Mexicans -- almost all of the Mexicans in the world are either in Mexico or the United States. So by combining our estimates of the number of Mexican immigrants in the U.S. legally and as unauthorized immigrants, plus the number of Mexicans in Mexico, we have a check on the total numbers.

During a speech at the American Legion National Convention in Cincinnati, Donald Trump spoke about his meeting with Mexican President Enrique Peña Nieto, saying he had expressed "deep respect" for the Mexican people. (The Washington Post)

THE FIX: The other part of that equation, then, is the number of immigrants that are here legally. How do you get that number?

PASSEL: Immigrants who are here legally are admitted as lawful permanent residents or as refugees through what is now the Department of Homeland Security. Each year the Department of Homeland Security publishes the number of immigrants they've admitted for lawful permanent residence. The other group that's admitted is refugees. Those are counted by the office of Refugee Resettlement in the Health and Human Services department.

So we take the number admitted each year and we add that to the previous year's estimate of lawful permanent residents. We update the estimate from year to year with basic demographic methodology: We take into account the new arrivals; we also make an estimate how many of last year's immigrants died in the previous year and how many moved out of the country.

PASSEL: The Census Bureau in every census does outreach to try to get people to participate. In both 2000 and 2010, there were a number of programs designed specifically to get Latinos to participate. It involved advertising, it involved working with community groups and various kinds of outreach.

The messages in the Census Bureau's advertising and outreach varied depending on which groups they were trying to get to participate. The unauthorized immigrant population is very heavily Hispanic. The Hispanic population, the Asian populations are very heavily immigrant. So the outreach to both the Hispanic population and the Asian population included messages in languages other than English and an emphasis on the confidential nature of the census and how important it is for local communities that people participate.

Based on the coverage studies of the last two censuses, those outreach programs were fairly successful, because the undercount as a percentage of the population was reduced substantially in 2000 and 2010 over what was experienced in 1990 and 1980.

THE FIX: So the natural question that people have is the extent to which this number could be wrong. We've got Donald Trump out there saying, "it could be anywhere between six and 30 million people." Setting that aside, why is it you feel as though a layperson can be confident that you're not off by up to 5 million immigrants?

PASSEL: What the Census Bureau is really pretty good at is counting houses. Houses don't move. It's hard for housing units to hide.

In the census and in the surveys, if a housing unit is occupied, the Census Bureau is able to count people in those housing units. They may not get everybody -- it's true that there may be more than one family unit in the household and they only get one. But overall, the studies we have of housing unit coverage and population coverage suggest it's very unlikely that the numbers could be a lot higher than what they are.

We build in a correction for undercount. So we're adjusting the numbers upward, and the adjustments are larger for the groups we know we tend to miss. We know we tend to miss young men more than young women and we know we miss young adults more than older adults. We're already factoring in an upward adjustment.

It's possible that the adjustment could be a bit more than what we're factoring in, but it's very, very unlikely that the numbers are as much as 5 million higher than what we've estimated.

As I said, the other check we have is looking at data on the Mexican population, age-by-age, adding the U.S. numbers to the Mexican numbers.

For instance, just a simple example -- we have a pretty good idea of how many Mexicans were born 25 years ago, and all of the 25-year-old Mexicans are essentially in the United States or in Mexico, so we can put our numbers together with the Mexican numbers and have confidence that the numbers aren't a lot higher than what we think they are.

THE FIX: So is it more likely that you're wrong by being too high rather than by being too low?

PASSEL: No, I think our estimates are pretty accurate.

We're working with sample-based data so the samples could be a little bit wrong but the base from which we adjust our numbers up is pretty -- we're pretty confident in that. It could possibly be a million or maybe a little more higher than where we're estimating. It could be lower by about that much. But it's probably more likely to be a little higher than what we're estimating than a little lower.

All in all we think they're pretty accurate. There are other people making estimates. They often use similar techniques, but there's a pretty wide consensus of numbers around 11 million from people who are looking at data.